Final answer:
The equation of the line passing through the points (7, -4) and (-1, 3) is y= -1/2 x - 11/2 Option A is correct.
Step-by-step explanation:
To find the equation of the line passing through the points (7, -4) and (-1, 3), we need to find the slope of the line first.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1)
Using the points (7, -4) and (-1, 3), we can substitute the values into the formula:
m = (3 - (-4)) / (-1 - 7) = 7/8
Now that we have the slope, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), and substitute one of the points to find the equation. Using the point (7, -4):
y - (-4) = (7/8)(x - 7)
y + 4 = (7/8)(x - 7)
y = (7/8)x - 49/8 - 32/8
y= -1/2 x - 11/2
Therefore, the equation of the line passing through the points (7, -4) and (-1, 3) is y= -1/2 x - 11/2.